Multilayer thin film attenuators

ABSTRACT

An optical element has layers formed on a substrate, including alternating first and second layers having first and second refractive indices, n L  and n H  that exhibit a spectral characteristic, providing, for incident light at a predetermined wavelength and directed toward the optical element within a range of angles bounded by first and second incident angles θ 1  and θ 2 , between 0 and 80 degrees and differing by at least 1 degree, substantially linear polarization-averaged attenuation of the incident light energy wherein, for any incident angle θ n  between θ 1  and θ 2 , Aθ n  is the corresponding polarization-averaged attenuation, and wherein the polarization-averaged attenuation at Aθ n  at angle θ 1  is less than or equal to an optical density value of 0.2 and the polarization-averaged attenuation Aθ n  at angle θ 2  exceeds an optical density value of 4.

FIELD OF THE INVENTION

This invention generally relates to variable optical attenuators and more particularly relates to an optical attenuator formed as a multilayer thin-film device and having reduced sensitivity to polarization.

BACKGROUND OF THE INVENTION

Variable light attenuators in the path of an emitted laser beam or other solid state light source enable efficient and stable operation of the light source while attenuating the light intensity to a suitable level for its application. A number of different approaches have been used for variable light attenuator design, including the use of spatially varying neutral density (ND) filters and other absorptive devices. One conventional method for variable light attenuation, as shown in FIG. 1A, employs the well known Malus' law. In this conventional arrangement, a laser attenuator 10 receives light from a laser light source 12, directed through a half-wave plate 14 and to a polarizing beamsplitter 16 or other polarizing element. Variable rotation of the half-wave plate about the optical axis enables a variable amount of the laser light to be transmitted through the polarizing element, with the remaining light directed to a light dump element 20 from the polarizing beamsplitter or absorbed by the polarizer.

Other attempts to develop variable laser light attenuators using multilayer thin-film technologies have proved disappointing. Among approaches that have been proposed is the use of a set of multilayer dielectric coated substrates having various reflectivity values. Each substrate is designed for a specific wavelength and provides a reflectance value for incident light of that wavelength. Installed at a slight angle to the beam, the attenuator reflects back some proportion of the light, as determined by the arrangement of dielectric layers.

One reason for the limited success of thin-film approaches relates to polarization. Practitioners in the optical arts have generalized the definitions of two mutually orthogonal polarization states as follows: light that has its polarization axis parallel to the plane of incidence is defined as having polarization state P, or P-polarized light; light that has its polarization axis perpendicular to the plane of incidence is defined as having polarization state S, or S-polarized light. For polarized light, the relative phase and amplitude of its P- and S-polarized components is fixed or constant. For un-polarized light, the relative phase and/or amplitude of P- and S-polarized components is random.

Conventional wisdom in thin-film design, reinforced by numerous practical examples, holds that multilayer thin-film surfaces are not polarization-neutral when light is not incident at a normal to the surface, but rather exhibit noticeable differences in their handling of light having different polarization axes. This principle is exploited in various designs, such as in the design of various types of polarizing beamsplitters. By way of illustration, FIG. 1B shows an exemplary transmission spectrum of a polarizing beamsplitter formed using thin-film coatings for two orthogonal polarization states. For one polarization state, shown as P-polarization, transmission is very high between wavelengths λ₁ and λ₂; for the other, S-polarization, most of the light in this range is reflected. A number of polarizing beamsplitter designs employ this same principle for separating light of different polarization states, over a given wavelength band.

Even where some attempt has been made to control the behavior of the different polarization states in a thin-film filter design, it has proved difficult to provide similar handling of light in S- and P-polarization states. By way of example, FIG. 1C shows the spectral characteristic of a high-performance edge filter having a relatively steep edge. Curves for P-polarized light P and S-polarized light S are shown, along with a curve for polarization-averaged light A, that is, the average of P- and S-polarized light. Transmission is shown from 0 dB (0 OD) to −100 dB (10 OD), over a range of angles of incidence (AOI) from 0 to 20 degrees. A difference curve D, shown as a dashed line and with its scale at the right, indicates the difference between attenuation for S- and P-polarized light at each point. As can be seen from FIG. 1C, this filter design provides nearly equivalent attenuation of both S- and P-polarized light within only a very limited range of angles, in the range from about 2 to 3 degrees. The attenuation then changes dramatically from that point, so that by about 4 degrees, the difference in attenuation as shown in curve D is about −5 dB (0.5 OD). Over an AOI range from greater than 2 to about 9 degrees, polarization-averaged attenuation ranges from 0 OD (0 dB) to 4 OD (−40 dB), as shown by curve A. However, over this same 7 degree angular range, the difference between attenuation to S— polarized light and attenuation to P-polarized light ranges from near 0 dB to about −16 dB (0 OD to 1.6 OD).

This problem in handling S- and P-polarized light differently has long been recognized by those skilled in thin-film filter design. As just one acknowledgement of the inherent problems caused by polarization, researchers Gu and Zheng, in an article entitled “Design of non-polarizing thin film edge filters” in Journal of Zhejiang University SCIENCE A (2006) 7(6) pp. 1037-1040, note the difficulty in dealing with polarization differences in thin-film response and state that “the separation between S- and P-polarization components is an invariable effect in such interference thin film edge filters at non-normal light incidence.” In addition, a number of patents and related publications also attest to this apparently inherent, invariable behavior, and some considerable effort has been expended in thin-film component design to try to correct or compensate for differences in handling light components of different polarization states. For example, U.S. Pat. No. 4,373,782 entitled “Non-Polarizing Thin-Film Edge Filter” to Thelen describes different behavior for light having P (parallel) and S (perpendicular) polarization axes and proposes aligning a single edge of an interference bandpass filter, at a fixed incident angle, to achieve similar response for P- and S-polarized light at a single wavelength or over a very narrow band of wavelengths. Other attempts try to address the problem of differences in how light of different polarization axes are handled by adjusting the position of polarization peaks for the different P- and S-polarization states, as described in U.S. Pat. No. 5,926,317 entitled “Multilayer Thin Film Dielectric Bandpass Filter” to Cushing, and in U.S. Patent Application No. 2003/0128432 entitled “Polarization Independent Thin Film Optical Interference Filters” by Cormack et al., for example.

A similar approach to that proposed in the Cushing '317 disclosure, matching polarization response for a single wavelength and fixed angle, is adapted for color separators and combiners by researchers Chen and Gu in an article entitled “Design of non-polarizing color splitting filters used for projection display system” in Displays 26 (April 2005) pp. 65-70. However, a combination of high dynamic range, high levels of attenuation, and insensitivity to polarization is not achieved, nor would it be useful with a spectral combiner or separator using such a coating. Notably, what these researchers teach provides neither linear attenuation response over a range of incident angles, nor similar attenuation for both S- and P-polarizations over a range of angles.

It is generally accepted that there is no way to surmount this problem; polarization differences are considered to be simply inherent to devices formed using layers of isotropic thin-film materials. In an article entitled “Nonpolarizing and polarizing filter design” in Applied Optics, 20 Apr. 2005, authors Qi et al., note that “changes in phase thicknesses and in optical admittances of the layers are fundamental and cannot be avoided at oblique incidence.” These authors also note that, as a result, different reflective and refractive properties are exhibited for the transverse-electric and transverse-magnetic fields of a plane wave in dielectric thin films. Their proposed solution for avoiding polarization-dependence is to use birefringent (i.e., nonisotropic) thin-film designs, which are considerably more difficult to fabricate than their isotropic counterparts.

Inherent differences in how thin-film coatings handle light having orthogonal polarization axes and experience with thin-film coatings in various filter applications offer little promise for non-polarized laser attenuation using these coatings. One example of a proposed solution is given in U.S. Pat. No. 4,778,263 entitled “Variable Laser Attenuator” to Foltyn that describes the use of a matched pair of thin-film interference filters arranged at different angles to provide variable laser attenuation. However, the Foltyn '263 disclosure clearly indicates a high degree of polarization dependence as well as wavelength dependence for an attenuation device formed in this manner, intended for use with unpolarized excimer lasers. Moreover, as is shown in FIG. 8 of the Foltyn '263 disclosure, the average light output is non-linear and may not even be monotonic over a range of incident angles.

Thus, there is a long-felt need for a variable laser attenuator that provides attenuation over a range of values and is polarization-neutral over that range.

SUMMARY OF THE INVENTION

It is an object of the present invention to advance the art of light attenuation. With this object in mind, the present invention provides apparatus and methods for polarization-independent attenuation of incident light using thin-film filters. According to an embodiment of the present invention, there is provided an optical element comprising:

-   -   at least one substrate having at least one surface;     -   and     -   a plurality of layers formed on the at least one surface of the         at least one substrate, the plurality of layers including         alternating first and second layers, the first layers having a         first refractive index, n_(L), and the second layers having a         second refractive index, n_(H), greater than the first         refractive index, wherein the plurality of layers exhibit a         spectral characteristic,     -   the spectral characteristic providing, for incident light at a         predetermined wavelength and directed toward the optical element         within a range of incident angles bounded by a first incident         angle θ₁ and a second incident angle θ₂,     -   wherein the first and second incident angles θ₁ and θ₂ are         between 0 and 80 degrees and wherein the difference between the         first and second incident angles θ₁ and θ₂ is at least 1 degree,         substantially linear polarization-averaged attenuation of the         incident light energy given by:         Aθ _(n)=−log₁₀((Tp _(n) +Ts _(n))/2)     -   wherein, for any incident angle θ_(n) that lies within the range         between and including angles θ₁ and θ₂,     -   Aθ_(n) is the corresponding polarization-averaged attenuation in         terms of optical density,     -   Tp_(n) is the transmission, at angle θ_(n), of light energy of a         first polarization axis, and     -   Ts_(n) is the transmission, at angle θ_(n), of light energy of a         second polarization axis that is orthogonal to the first         polarization axis, and     -   wherein the polarization-averaged attenuation Aθ_(n) at angle θ₁         is less than or equal to an optical density value of 0.2 and the         polarization-averaged attenuation Aθ_(n) at angle θ₂ exceeds an         optical density value of 4.

It is a feature of the present invention that it provides optical attenuation that varies with angle of incidence over a range of angles.

It is an advantage of the present invention that it provides optical polarization-averaged attenuation of laser or other narrow-band light with a single optical element. Embodiments of the present invention do not require birefringent or otherwise nonisotropic film layers, but use conventional isotropic dichroic thin film materials for providing laser light attenuation that is polarization-independent.

These and other aspects, objects, features and advantages of the present invention will be more clearly understood and appreciated from a review of the following detailed description of the preferred embodiments and appended claims, and by reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

While the specification concludes with claims particularly pointing out and distinctly claiming the subject matter of the present invention, it is believed that the invention will be better understood from the following description when taken in conjunction with the accompanying drawings.

FIG. 1A is a schematic diagram showing a conventional type of laser attenuator using a half wave plate and polarizing beamsplitter.

FIG. 1B is a graph showing an exemplary transmission spectrum of a polarizing beamsplitter formed using thin-film coatings for two orthogonal polarization states.

FIG. 1C is a graph that shows characteristic attenuation that can be achieved using a conventional edge filter formed from multi-layer thin film coatings.

FIG. 2 is a schematic diagram that shows an optical element for light attenuation over a range of incident angles.

FIG. 3 is a diagram showing graphs of attenuation arrangements for linear attenuation of the average of two orthogonal polarization states.

FIG. 4 is a diagram showing graphs of attenuation of the average of two orthogonal polarization states and of the S- and P-polarized components.

FIG. 5 is a graph that shows the spectral characteristic for a variable attenuator in an embodiment of the present invention for incident light of a given wavelength.

FIG. 6A is a graph that shows a spectral characteristic for a highly linear embodiment, in which both of the respective attenuation curves for S- and P-polarized light are linear over the given incident angle range.

FIG. 6B is a graph that shows deviation from linear attenuation for S- and P-polarized light on an enlarged scale for the embodiment shown in FIG. 6A.

FIG. 7A is a graph that shows a spectral characteristic for another highly linear embodiment, in which both of the respective attenuation curves for S- and P-polarized light are linear with positive slope over the given incident angle range.

FIG. 7B is a graph that shows deviation curves for S- and P-polarized light respectively, showing, on an enlarged scale, deviation from linear for the embodiment shown in FIG. 7A.

FIG. 8 shows spectral characteristics for light having different cone half-angles according to an embodiment of the present invention.

FIG. 9 is a spectral characteristic of a variable attenuator having a linear response over a range of angles, with percent transmission shown.

DETAILED DESCRIPTION OF THE INVENTION

The present description is directed in particular to elements forming part of, or cooperating more directly with, apparatus in accordance with the invention. It is to be understood that elements not specifically shown or described may take various forms well known to those skilled in the art.

Figures shown and described herein are provided in order to illustrate key principles of operation and component relationships along their respective optical paths according to the present invention and are not drawn with intent to show actual size or scale. Some exaggeration may be necessary in order to more clearly emphasize basic structural relationships or principles of operation. Some conventional components that would be needed for implementation of the described embodiments, such as various types of optical mounts and related hardware, for example, are well known and are not shown in the drawings in order to simplify description of the invention itself. In the drawings and text that follow, like components are designated with like reference numerals, and similar descriptions concerning components and arrangement or interaction of components already described are omitted. Where they are used, the terms “first”, “second”, “third”, and so on, do not necessarily denote any ordinal or priority relation, but are simply used to more clearly distinguish one element from another.

As was noted in the background section, multilayer thin film optical elements formed using isotropic layers have been heretofore considered to be poorly suited for use as variable laser light attenuators, due largely to polarization effects. In spite of conventional teaching for thin-film devices, embodiments of the present invention adapt thin-film design to the problem of variable light attenuation and provide a variable light attenuator that provides a high level of attenuation for light of a given wavelength and that is capable of providing variable light attenuation with both polarized and un-polarized light.

Variable Attenuation by Incident Angle

Embodiments of the present invention provide an optical element that presents a variable polarization-averaged attenuation to incident light at a given wavelength according to the angle of incidence of the light beam on the optical element. As shown in the schematic diagram of FIG. 2, the angle of incidence of a light beam from light source 12 to an optical element 30 that provides the attenuation can be varied to any suitable angle θn in a range that is bounded by two angular values, shown as θ₁ and θ₂. The range of angles of incidence can be over some portion of the range from 0 to about 80 degrees, so that incident light can have a normal, near-normal, or non-normal relationship to the surface of optical element 30 at various positions in the angular range. In the context of the present disclosure, an angular relationship is considered to be “non-normal” when not within ±10 degrees of any integer multiple of 90 degrees.

The performance of optical element 30 is determined by the design of multiple thin-film layers that provide or exhibit a spectral characteristic. Inset E in FIG. 2 shows layers 80 a 1, 80 a 2 . . . 80 z 1, 80 z 2, formed on at least one surface of a transparent substrate 70, that provide the spectral characteristic. The layers are formed of transparent isotropic materials with alternating first layers having a first refractive index, n_(L), and second layers having a second refractive index, n_(H), greater than the first refractive index, wherein the plurality of layers exhibits a spectral characteristic.

FIG. 3 shows graphs 46, 48, 50, 52, and 54 of possible attenuation arrangements that can be provided between angles θ₁ and θ₂ as part of the spectral characteristic obtained by the arrangement of layers 80 a 1, 80 a 2 . . . 80 z 1, 80 z 2. Incident light is at a fixed, predetermined wavelength, depending on the laser or other light source for which the attenuator is designed.

Graph 48 in FIG. 3 shows an attenuation curve 58 that is monotonic and substantially linear, so that a change in incident angle θn causes a proportional change in attenuation, to within some tolerance. Linearity is a monotonic relationship by definition. Each of graphs 50, 52, and 54 show linear attenuation of the incident light energy for the average of S- and P-polarized light components. Graph 48 shows attenuation having a linear or substantially linear relation. Graph 46 shows attenuation that is monotonic, but may or may not be substantially linear, as defined herein.

The attenuation curves 48, 50, 52, and 54 of FIG. 3 provide a monotonic, linear polarization-averaged attenuation characteristic for the incident light energy over a predefined attenuation range, shown here in terms of optical density (OD) from 0 to 6 OD, correspondingly from 0 dB attenuation to −60 dB attenuation. Optical density in OD is defined as −log₁₀(Transmission). Attenuation in dB is defined as 10×log₁₀(Transmission). Transmission is assumed to vary between 0 (no transmission) and 1 (100% transmission). It should be noted that attenuation is expressed as a positive number in OD, but often graphed with opposite slope as shown in FIG. 3. Attenuation in dB is expressed as a negative value.

In the particular relationship shown in these example graphs, an increase in angle θn within the range causes an increase in attenuation; the slope of the attenuation curve could alternately be in the opposite direction, with attenuation at a lower value as angle θ_(n) increases.

Each of graphs 48, 50, 52, 54, and 46 show monotonic attenuation of the incident light energy for the average of S- and P-polarized light components given by: Aθ _(n)=−log₁₀((Tp _(n) +Ts _(n))/2)  (1)

-   -   wherein, for any incident angle θ_(n) that lies within the range         between and including angles θ₁ and θ₂,     -   Aθ_(n) is the corresponding polarization-averaged attenuation;     -   Tp_(n) is the transmission of light energy at angle θ_(n) of a         first polarization axis, such as P-polarized light; and     -   Ts_(n) is the transmission of light energy at angle θ_(n) of a         second polarization axis that is orthogonal to the first         polarization axis.

In graph 50, curves S and P for the S-polarized light and P-polarized light also show monotonic behavior over the interval between incident angles θ₁ and θ₂. In graph 52, neither the attenuation curve S for S-polarized light nor the attenuation curve P for P-polarized light are monotonic over the range between incident angles θ₁ and θ₂; however, their average attenuation A is monotonic and substantially linear. In graph 54, both the attenuation curve for P-polarized light component, P, and the attenuation curve for S-polarized light component, S, are monotonic over the range between incident angles θ₁ and θ₂; and substantially linear, as defined herein, as well as close together in value over the range. In graph 46, both the attenuation curve for P-polarized light component, P, and the attenuation curve for S-polarized light component, S, are monotonic over the range between incident angles θ₁ and θ₂, as well as close together in value over the range, despite the fact that the polarized-averaged attenuation may not be substantially linear. For example, at any angle θ_(n) in the range, the difference between attenuation values Ap_(n) and As_(n) for S- and P-polarized light is less than or equal to 0.1 OD (1 dB), preferably less than 0.02 OD (0.2 dB), more preferably less than 0.01 OD (0.1 dB).

In the context of the present disclosure, the term “linear” relates to the relationship between two related values and to how one value changes with respect to another. First and second values are related in a linear manner when there is a proportional relationship between them that is substantially fixed. Values that are proportional change in a fixed ratio, so that an amount of change to the first variable determines a proportional amount of change to the second variable.

The slope of linear attenuation can be positive or negative in different embodiments of the present invention. For consistency in the context of the present disclosure, the angle θ₂ is defined as the angle at which attenuation is greater; the angle θ₁ is the angle at which attenuation is near zero. Thus, in an embodiment of the present invention, angle θ₂ may be greater than or less than θ₁, depending on the spectral characteristic that is provided by a particular filter design. Using this definition, in the context of the present disclosure, “substantially linear attenuation” is defined relative to the proportion (slope) m that is defined by:

$\begin{matrix} {m = \frac{A\;\theta_{2}}{\theta_{2} - \theta_{1}}} & \left( {2a} \right) \end{matrix}$ wherein Aθ₂ is the actual polarization-averaged attenuation value at θ₂, expressed in OD. The actual attenuation value at θ₁, Aθ₁, is zero or very near zero, to at least within the range: Aθ ₁≦0.2 OD  (2b) Preferably, the attenuation value Aθ₁ is even closer to zero, such as: Aθ ₁≦0.1 OD  (2c)

Perfectly linear attenuation at angle θ_(n) is taken to be Aθ _(n,linear) =m(θ_(n)−θ₁)  (2d) wherein by definition the attenuation is taken to be exactly 0 at θ₁. The actual measured polarization-averaged attenuation value, in OD, is considered to be substantially linearly related when it satisfies, at every angle θ_(n) in the range: −0.02 OD≦Aθ _(n) −Aθ _(n,linear)+0.02 OD, or, explicitly, −0.02 OD≦Aθ _(n) −m(θ_(n)−θ₁)≦+0.02 OD.  (3)

Thus, for example, the exemplary edge filter whose spectral characteristic is shown in FIG. 1C does not exhibit substantially linear polarization-averaged attenuation over the range from 0 OD to 4 OD, as defined herein. To show this for the example of FIG. 1C, observe that the polarization-averaged attenuation value Aθ₁ at approximately 0 degrees, is Aθ₁=0 OD. The polarization-averaged attenuation value Aθ₂ at 9 degrees is Aθ₂=4 OD. Using equation (2a) above, this yields the slope

$m = {\frac{4}{9 - 0} = 0.444}$ Then, consider a value θ_(n) within the range; for example where θ_(n)=6 degrees, Aθ_(n)=1.9 OD. To use (3), compute: Aθ _(n) −m(θ_(n)−θ₁)=1.9−0.444(6−0)=−0.764 OD This shows that relation (3) is not properly met for all angles θ_(n) within the range defined by θ₁ and θ₂ by the spectral characteristic of the edge filter given in FIG. 1C.

Thus, for example, polarization-averaged curve A in graph 46 of FIG. 3 may be substantially linear provided each value Aθ_(n) on the curve meets these criteria. This same relationship in (2a-d) and (3), with the necessary changes of terms, also defines whether or not individual attenuation curves for P-polarized and S-polarized light, labeled S and P respectively, can be considered to be substantially linear.

In addition to linearity, attenuator embodiments of the present invention also provide polarization insensitivity wherein the S-polarized light and P-polarized light are closely matched over a range of angles, with their respective attenuation values differing from each other at any angle θ_(n) by not more than about 0.1 OD, which can be stated: −0.1 OD≦Ap _(n) −As _(n)≦+0.1 OD  (4) for any angle θ_(n) between θ₁ and θ₂. Preferably, Ap_(n) and As_(n) differ from each other by no more than about 0.02 OD. More preferably, values Ap_(n) and As_(n) differ from each other by no more than about 0.01 OD. This close-match relationship is shown in FIG. 4. An inset K1 shows this proximity of S- and P-attenuation values for a linear average curve 58. For a graph 60, another inset K2 shows this proximity of values for a monotonic average curve 56.

The graph of FIG. 5 shows the spectral characteristic for a variable attenuator in an embodiment of the present invention for light of a given wavelength of 532 nm, wherein the range of angles is defined about a central angle of approximately 45 degrees. The attenuation curve for average polarization, A, is substantially linear over the range of angles of incidence (AOI) from 40 to 50 degrees, with attenuation ranging from 0 OD (equivalent to 0 dB) to 6 OD (equivalent to −60 dB). The individual attenuation curves for the P-polarized light component, P, and for the S-polarized light component, S, are not linear in this embodiment. Also plotted in FIG. 5 is a difference curve D that indicates the difference, in dB, between the actual polarization-averaged attenuation curve and the idealized, perfectly linear attenuation curve varying from OD 0 to 6 over the angular range 40 to 50 degrees. Table 1 lists the layer components used to provide the spectral characteristic shown in FIG. 5.

The graph of FIG. 6A shows a spectral characteristic for a highly linear embodiment, in which both of the respective attenuation curves for S- and P-polarized light are linear over the given AOI range. Again, the difference curve D shows the difference, in dB, between an actual polarization-averaged attenuation curve and an idealized, perfectly linear attenuation curve varying from OD 0 to 6 over the angular range 40 to 50 degrees. The graph of FIG. 6B shows deviation from linear with deviation curves DS and DP for S- and P-polarized light respectively, on an enlarged scale. As can be seen, the deviation over the angular range is within ±0.2 dB (±0.02 OD), indicating substantial linearity. Table 2 lists the layer components used to provide the spectral characteristic shown in FIGS. 6A and 6B.

The graph of FIG. 7A shows a spectral characteristic exhibited for a highly linear embodiment with opposite slope from that shown in FIG. 6A, in which again both of the respective attenuation curves for S- and P-polarized light are linear over the given AOI range. Again, the difference curve D shows the difference, in dB, between the actual polarization-averaged attenuation curve and the idealized, perfectly linear attenuation curve varying from OD 6 to 0 over the angular range 40 to 50 degrees. The graph of FIG. 7B shows deviation curves DS and DP for S- and P-polarized light respectively, on an enlarged scale. As can be seen from FIG. 7A, the difference over the range is within about ±0.3 dB (±0.03 OD), with substantial linearity of the average curve. Deviation from linear, shown in FIG. 7B, is within ±0.2 dB (±0.02 OD) for each individual S and P light component. Table 3 lists the layer components used to provide the spectral characteristic shown in FIGS. 7A and 7B.

Significantly, embodiments of the present invention provide a spectral characteristic that provides attenuation of 4 OD (−40 dB) or better for a variable optical attenuator at angles of incidence over a range of 1 degree or more. For even greater performance, embodiments of the present invention provide a spectral characteristic with attenuation of up to 6 OD (−60 dB) for a variable optical attenuator at angles of incidence over a range of up to 1 degree or greater.

One consideration for a variable attenuator with the advantageous polarization-handling characteristics of embodiments of the present invention relates to the angular range of the incident light beam. The graph of FIG. 8 shows how the spectral characteristic of the thin-film attenuator of embodiments of the present invention provides a similar spectral characteristic for light having successively larger cone half-angles (CHA). FIG. 8 shows spectral characteristic performance for light having 10 degree CHA. Table 4 lists the layer components used to provide the spectral characteristic shown in FIG. 8.

The graph of FIG. 9 shows an embodiment having linear transmission (in percentage) over a broad range of angles of incidence. Table 5 lists the layer components used to provide the spectral characteristic shown in FIG. 9.

Thin-Film Arrangements

Exemplary filters consistent with the invention and having the characteristics illustrated in FIGS. 5-9 may be produced by depositing hard coating filter layers using a timing technique and an ion-assisted, ion-beam sputtering vacuum system. The filters may be deposited on a Schott OG-570 glass substrate, the low-index material may be silicon dioxide (SiO2, index of about 1.5), and the high-index material may be tantalum pentoxide (Ta2O₅, index of about 2.1).

The layer structure for the variable attenuator with the spectral characteristic of FIG. 5 is provided subsequently in Table 1.

The layer structure for the variable attenuator with the spectral characteristic of FIGS. 6A and 6B is provided subsequently in Table 2.

The layer structure for the variable attenuator with the spectral characteristic of FIGS. 7A and 7B is provided subsequently in Table 3.

The layer structure for the variable attenuator with the spectral characteristic of FIG. 8 is provided subsequently in Table 4.

The layer structure for the variable attenuator with the spectral characteristic of FIG. 9 is provided subsequently in Table 5.

Fabrication Methods

Multilayer thin-film attenuators of the present invention use optically isotropic coatings of metal oxides that are physically hard (“hard coatings”) and provide a glass-like surface, as opposed to optical coatings of softer materials, such as sodium aluminum fluoride (“cryolite”) and/or zinc sulfide (“soft coatings”). For example, filters including soft coatings are commercially available from Omega Optical, Inc.

In a preferred embodiment, the hard coating layers are deposited using ion-assisted ion beam sputtering. In order to reproducibly make filters with hard coating layers, given that the deposition rate in most deposition systems may vary with time, it is useful to use an optical monitoring technique. For example, commonly assigned U.S. Pat. No. 7,068,430 to Clarke et al., incorporated herein by reference, discusses optical monitoring methods which can be used to make the inventive filters. However, in ion-beam sputtering systems the deposition rate can be remarkably stable, and therefore when such a machine is running well, the hard coating layers may be deposited by calculating the thickness desired for each layer, assuming a deposition rate for each material, and then using the resulting deposition time to determine when to cut each layer (a “timing” technique). Those skilled in the art will recognize, however, that other deposition systems, such as ion-assisted electron beam evaporation and magnetron sputtering, may be used to deposit the layers. Also, a variety of “hard coating” materials that may be used as the high and low index of refraction layers will also be known to those skilled in the art. Exemplary hard coating materials include: SiO₂ (refractive index 1.5); TiO₂ (refractive index 2.4); Ta₂O₅ (refractive index 2.1); Nb₂O₅ (refractive index 2.2); HfO₂ (refractive index about 2.0); and Al₂O₅.

It is to be understood that the terms “high index of refraction” and “low index of refraction” are used herein to indicate a relative difference between the two layers of material (high and low), and, do not necessarily indicate a particular range of indexes. Thus, each high index of refraction layer need only have an index of refraction which is numerically higher than the low index of refraction layer adjacent thereto. The numerical differences between the index of refraction in the high and low index of refraction materials affects the number of layers required for forming a filter with a particular transmittance characteristic. Generally, a small difference between the indices of refraction in the high and low index materials requires a higher number of alternating layers to achieve a particular transmittance (or optical density) than would be required with a larger difference.

Each of the layers shown as 80 a 1, 80 a 2 . . . 80 z 1, 80 z 2 in FIG. 2 has an associated optical thickness, defined by the product of its physical thickness times its refractive index. Although the embodiments shown in the drawings are not drawn to scale, the hard coating layers illustrated in FIG. 2 may be, for example, one quarter wavelength in optical thickness. Depending on desired transmission characteristics, however, non-quarter-wave optical thicknesses and/or varying optical thicknesses may also be provided. Layers may be provided on one or both surfaces of the substrate. One surface of the substrate may have an additional anti-reflection coating.

Earlier multilayer surface designs may have spectral characteristics wherein the averaged transmission of light is monotonic or linear over a very narrow range of wavelengths and incident angles, and wherein the attenuation provided to light may not be variable by more than 2 OD over that narrow angular range. By contrast, the spectral characteristic of embodiments of the present invention provide monotonic and substantially linear attenuation in excess of 2 OD over an angular range as high as ±5 degrees or more from a central angle. This angular spread, with monotonic and linear attenuation, is advantageous because it allows attenuation to be easily adjusted with rotation of a surface on an axis orthogonal to the incident beam. Furthermore, a larger angular range to achieve a given range of attenuation (i.e., smaller slope m in Equation 2a), enables a beam of light with less collimation (larger cone-half-angle) to pass through the attenuator with minimal attenuation at one end of the angular range, while maintaining polarization-neutral and substantially linear attenuation over the predominant portion of the dynamic range. Linear attenuation over a range of angles can be particularly useful where it is desirable to change beam intensity in a controlled way, over time.

As is known to those skilled in the thin-film coating arts, there is a correspondence between change in incident angle and shift in wavelength. This allows a multilayer thin-film design of a variable attenuator, designed for a target wavelength, to be readily adaptable and usable with light of nearby wavelengths.

Embodiments of the present invention are suited for attenuation of laser light or other narrow-beam light having a specified wavelength or narrow range of wavelengths. The optical element of the present invention can be used with polarized as well as non-polarized or randomly polarized light. The optical element of the present invention can be fixtured to rotate over a range of incident angles under automatic or manual control.

Thus, what is provided is an apparatus and method for providing a variable multilayer thin film attenuator.

TABLE 1 FIG. 5 Layer Arrangement Coating Thickness (μm): 8.332 Nb2O5 (μm): 2.644 SiO2 (μm): 5.688 Total Layers: 110 Layer Material Thickness (nm) 1 Nb2O5 59.1 2 SiO2 98.0 3 Nb2O5 54.5 4 SiO2 90.2 5 Nb2O5 48.2 6 SiO2 67.4 7 Nb2O5 43.8 8 SiO2 66.3 9 Nb2O5 48.0 10 SiO2 83.9 11 Nb2O5 55.2 12 SiO2 97.6 13 Nb2O5 58.7 14 SiO2 103.4 15 Nb2O5 60.4 16 SiO2 97.2 17 Nb2O5 59.5 18 SiO2 82.1 19 Nb2O5 46.9 20 SiO2 62.9 21 Nb2O5 38.1 22 SiO2 75.5 23 Nb2O5 49.9 24 SiO2 95.3 25 Nb2O5 57.9 26 SiO2 104.6 27 Nb2O5 59.3 28 SiO2 108.5 29 Nb2O5 58.0 30 SiO2 110.8 31 Nb2O5 56.9 32 SiO2 113.1 33 Nb2O5 51.6 34 SiO2 103.6 35 Nb2O5 31.3 36 SiO2 65.5 37 Nb2O5 29.5 38 SiO2 99.6 39 Nb2O5 53.5 40 SiO2 107.6 41 Nb2O5 58.9 42 SiO2 109.0 43 Nb2O5 58.3 44 SiO2 110.1 45 Nb2O5 58.5 46 SiO2 111.2 47 Nb2O5 57.6 48 SiO2 113.5 49 Nb2O5 56.8 50 SiO2 118.4 51 Nb2O5 51.8 52 SiO2 138.7 53 Nb2O5 25.8 54 SiO2 74.1 55 Nb2O5 1.9 56 SiO2 146.2 57 Nb2O5 44.2 58 SiO2 117.5 59 Nb2O5 53.9 60 SiO2 114.1 61 Nb2O5 55.7 62 SiO2 110.2 63 Nb2O5 56.0 64 SiO2 109.0 65 Nb2O5 56.4 66 SiO2 107.5 67 Nb2O5 52.2 68 SiO2 97.5 69 Nb2O5 37.3 70 SiO2 71.3 71 Nb2O5 33.4 72 SiO2 90.9 73 Nb2O5 49.9 74 SiO2 103.9 75 Nb2O5 59.7 76 SiO2 106.3 77 Nb2O5 58.7 78 SiO2 108.6 79 Nb2O5 52.0 80 SiO2 95.3 81 Nb2O5 43.1 82 SiO2 69.1 83 Nb2O5 35.8 84 SiO2 77.4 85 Nb2O5 47.1 86 SiO2 100.2 87 Nb2O5 56.1 88 SiO2 103.3 89 Nb2O5 59.2 90 SiO2 105.7 91 Nb2O5 54.6 92 SiO2 108.6 93 Nb2O5 31.2 94 SiO2 82.8 95 Nb2O5 22.3 96 SiO2 109.2 97 Nb2O5 47.7 98 SiO2 108.6 99 Nb2O5 59.0 100 SiO2 101.0 101 Nb2O5 60.8 102 SiO2 86.3 103 Nb2O5 46.6 104 SiO2 59.2 105 Nb2O5 1.7 106 SiO2 194.6 107 Nb2O5 19.9 108 SiO2 120.8 109 Nb2O5 59.3 110 SiO2 274.7

TABLE 2 FIG. 6A/6B Layer Arrangement Coating Thickness (μm): 9.275 Nb2O5 (μm): 3.175 SiO2 (μm): 6.099 Total Layers: 118 Layer Material Thickness (nm) 1 Nb2O5 57.70035 2 SiO2 90.5859 3 Nb2O5 48.87371 4 SiO2 64.49805 5 Nb2O5 161.5009 6 SiO2 64.70093 7 Nb2O5 48.22371 8 SiO2 89.58865 9 Nb2O5 57.16394 10 SiO2 101.9997 11 Nb2O5 56.42101 12 SiO2 105.5099 13 Nb2O5 50.50218 14 SiO2 93.65918 15 Nb2O5 25.03022 16 SiO2 80.55084 17 Nb2O5 36.74455 18 SiO2 99.71027 19 Nb2O5 51.46165 20 SiO2 121.0438 21 Nb2O5 57.30858 22 SiO2 111.2526 23 Nb2O5 56.98762 24 SiO2 101.2778 25 Nb2O5 54.40687 26 SiO2 82.7682 27 Nb2O5 39.01113 28 SiO2 60.75344 29 Nb2O5 39.71163 30 SiO2 85.46865 31 Nb2O5 54.73308 32 SiO2 101.9909 33 Nb2O5 59.89734 34 SiO2 107.2912 35 Nb2O5 59.09109 36 SiO2 108.8334 37 Nb2O5 59.99157 38 SiO2 108.6467 39 Nb2O5 56.04696 40 SiO2 102.9672 41 Nb2O5 47.60399 42 SiO2 72.93378 43 Nb2O5 29.59962 44 SiO2 70.52065 45 Nb2O5 46.06779 46 SiO2 102.1195 47 Nb2O5 55.28625 48 SiO2 113.2163 49 Nb2O5 57.57183 50 SiO2 117.3189 51 Nb2O5 57.34705 52 SiO2 118.7372 53 Nb2O5 57.87605 54 SiO2 118.2473 55 Nb2O5 57.80588 56 SiO2 115.2186 57 Nb2O5 56.22888 58 SiO2 107.3296 59 Nb2O5 50.31733 60 SiO2 80.57623 61 Nb2O5 29.04926 62 SiO2 67.64751 63 Nb2O5 39.90681 64 SiO2 99.93217 65 Nb2O5 54.4226 66 SiO2 113.624 67 Nb2O5 55.93844 68 SiO2 117.4483 69 Nb2O5 56.66708 70 SiO2 115.3602 71 Nb2O5 58.70031 72 SiO2 113.8126 73 Nb2O5 55.03245 74 SiO2 109.3527 75 Nb2O5 53.71783 76 SiO2 87.78038 77 Nb2O5 44.00093 78 SiO2 61.97066 79 Nb2O5 40.07847 80 SiO2 72.65181 81 Nb2O5 53.44348 82 SiO2 99.99185 83 Nb2O5 58.25613 84 SiO2 105.2992 85 Nb2O5 59.27326 86 SiO2 103.3531 87 Nb2O5 57.33131 88 SiO2 92.65092 89 Nb2O5 47.56535 90 SiO2 72.87523 91 Nb2O5 37.25349 92 SiO2 69.74638 93 Nb2O5 47.11861 94 SiO2 92.44581 95 Nb2O5 57.22467 96 SiO2 100.4564 97 Nb2O5 57.86897 98 SiO2 100.8269 99 Nb2O5 55.05754 100 SiO2 92.59423 101 Nb2O5 39.972 102 SiO2 63.17161 103 Nb2O5 35.08632 104 SiO2 300.2094 105 Nb2O5 52.89133 106 SiO2 100.9649 107 Nb2O5 57.19679 108 SiO2 108.3576 109 Nb2O5 54.56803 110 SiO2 119.8437 111 Nb2O5 143.8859 112 SiO2 68.05159 113 Nb2O5 15.98383 114 SiO2 144.4671 115 Nb2O5 54.58889 116 SiO2 109.6031 117 Nb2O5 56.89793 118 SiO2 295.4826

TABLE 3 FIG. 7A/7B Layer Arrangement Coating Thickness (μm): 11.71 Nb2O5 (μm): 4.736 SiO2 (μm): 6.974 Total Layers: 130 Layer Material Thickness (nm) 1 Nb2O5 58.4 2 SiO2 116.8 3 Nb2O5 141.3 4 SiO2 250.4 5 Nb2O5 58.4 6 SiO2 109.6 7 Nb2O5 173.8 8 SiO2 108.2 9 Nb2O5 51.2 10 SiO2 130.7 11 Nb2O5 117.8 12 SiO2 120.0 13 Nb2O5 43.6 14 SiO2 112.9 15 Nb2O5 56.1 16 SiO2 119.7 17 Nb2O5 72.3 18 SiO2 185.0 19 Nb2O5 70.3 20 SiO2 114.9 21 Nb2O5 58.2 22 SiO2 104.8 23 Nb2O5 56.8 24 SiO2 108.7 25 Nb2O5 57.7 26 SiO2 422.9 27 Nb2O5 56.7 28 SiO2 108.5 29 Nb2O5 56.4 30 SiO2 102.5 31 Nb2O5 59.2 32 SiO2 112.3 33 Nb2O5 72.4 34 SiO2 180.9 35 Nb2O5 193.6 36 SiO2 110.7 37 Nb2O5 60.2 38 SiO2 100.5 39 Nb2O5 60.9 40 SiO2 100.4 41 Nb2O5 65.2 42 SiO2 113.3 43 Nb2O5 80.6 44 SiO2 149.8 45 Nb2O5 201.6 46 SiO2 115.9 47 Nb2O5 66.8 48 SiO2 100.2 49 Nb2O5 60.9 50 SiO2 97.4 51 Nb2O5 58.4 52 SiO2 97.6 53 Nb2O5 59.2 54 SiO2 99.9 55 Nb2O5 62.8 56 SiO2 116.8 57 Nb2O5 87.4 58 SiO2 157.0 59 Nb2O5 74.3 60 SiO2 108.6 61 Nb2O5 63.0 62 SiO2 95.2 63 Nb2O5 59.7 64 SiO2 95.6 65 Nb2O5 60.3 66 SiO2 91.1 67 Nb2O5 60.5 68 SiO2 81.4 69 Nb2O5 58.6 70 SiO2 71.4 71 Nb2O5 55.3 72 SiO2 64.8 73 Nb2O5 54.0 74 SiO2 62.5 75 Nb2O5 54.5 76 SiO2 64.5 77 Nb2O5 55.6 78 SiO2 72.2 79 Nb2O5 59.2 80 SiO2 83.8 81 Nb2O5 179.9 82 SiO2 96.2 83 Nb2O5 71.7 84 SiO2 123.0 85 Nb2O5 89.5 86 SiO2 132.6 87 Nb2O5 81.3 88 SiO2 107.2 89 Nb2O5 64.2 90 SiO2 98.8 91 Nb2O5 60.3 92 SiO2 82.4 93 Nb2O5 58.4 94 SiO2 71.8 95 Nb2O5 55.8 96 SiO2 65.4 97 Nb2O5 55.1 98 SiO2 64.6 99 Nb2O5 53.8 100 SiO2 65.1 101 Nb2O5 55.6 102 SiO2 67.9 103 Nb2O5 57.2 104 SiO2 76.3 105 Nb2O5 59.6 106 SiO2 87.9 107 Nb2O5 63.5 108 SiO2 100.1 109 Nb2O5 71.5 110 SiO2 139.9 111 Nb2O5 90.1 112 SiO2 128.4 113 Nb2O5 71.9 114 SiO2 102.4 115 Nb2O5 57.6 116 SiO2 91.3 117 Nb2O5 164.6 118 SiO2 76.4 119 Nb2O5 48.5 120 SiO2 73.1 121 Nb2O5 52.2 122 SiO2 73.4 123 Nb2O5 54.2 124 SiO2 72.6 125 Nb2O5 50.2 126 SiO2 69.0 127 Nb2O5 44.6 128 SiO2 72.4 129 Nb2O5 51.4 130 SiO2 76.4

TABLE 4 FIG. 8 Layer Arrangement Coating Thickness (μm): 9.065 Nb2O5 (μm): 3.541 SiO2 (μm): 5.523 Total Layers: 122 Layer Material Thickness (nm) 1 Nb2O5 27.4 2 SiO2 240.0 3 Nb2O5 43.3 4 SiO2 110.2 5 Nb2O5 40.2 6 SiO2 106.0 7 Nb2O5 132.7 8 SiO2 97.2 9 Nb2O5 35.2 10 SiO2 116.3 11 Nb2O5 49.8 12 SiO2 111.9 13 Nb2O5 46.9 14 SiO2 101.3 15 Nb2O5 21.4 16 SiO2 74.5 17 Nb2O5 37.6 18 SiO2 112.7 19 Nb2O5 53.4 20 SiO2 119.7 21 Nb2O5 54.0 22 SiO2 105.2 23 Nb2O5 44.8 24 SiO2 74.9 25 Nb2O5 27.4 26 SiO2 81.5 27 Nb2O5 45.7 28 SiO2 102.5 29 Nb2O5 56.2 30 SiO2 102.4 31 Nb2O5 55.7 32 SiO2 102.3 33 Nb2O5 45.1 34 SiO2 73.4 35 Nb2O5 32.1 36 SiO2 76.3 37 Nb2O5 44.6 38 SiO2 102.3 39 Nb2O5 55.2 40 SiO2 103.8 41 Nb2O5 58.3 42 SiO2 91.7 43 Nb2O5 52.0 44 SiO2 73.2 45 Nb2O5 41.3 46 SiO2 62.3 47 Nb2O5 46.5 48 SiO2 81.4 49 Nb2O5 56.8 50 SiO2 97.0 51 Nb2O5 60.1 52 SiO2 94.4 53 Nb2O5 57.2 54 SiO2 78.1 55 Nb2O5 49.2 56 SiO2 62.0 57 Nb2O5 44.3 58 SiO2 65.3 59 Nb2O5 52.5 60 SiO2 86.7 61 Nb2O5 59.7 62 SiO2 93.1 63 Nb2O5 60.8 64 SiO2 86.3 65 Nb2O5 56.4 66 SiO2 69.6 67 Nb2O5 50.0 68 SiO2 57.9 69 Nb2O5 47.8 70 SiO2 65.5 71 Nb2O5 54.9 72 SiO2 82.5 73 Nb2O5 60.7 74 SiO2 93.6 75 Nb2O5 61.7 76 SiO2 92.7 77 Nb2O5 179.4 78 SiO2 78.8 79 Nb2O5 48.4 80 SiO2 55.1 81 Nb2O5 45.3 82 SiO2 64.3 83 Nb2O5 52.1 84 SiO2 85.2 85 Nb2O5 59.8 86 SiO2 96.5 87 Nb2O5 61.7 88 SiO2 100.2 89 Nb2O5 61.8 90 SiO2 101.6 91 Nb2O5 61.2 92 SiO2 101.7 93 Nb2O5 58.1 94 SiO2 92.2 95 Nb2O5 164.1 96 SiO2 51.0 97 Nb2O5 31.7 98 SiO2 83.9 99 Nb2O5 39.0 100 SiO2 117.4 101 Nb2O5 54.4 102 SiO2 116.5 103 Nb2O5 58.2 104 SiO2 104.1 105 Nb2O5 63.0 106 SiO2 97.4 107 Nb2O5 64.4 108 SiO2 90.9 109 Nb2O5 62.5 110 SiO2 78.6 111 Nb2O5 55.1 112 SiO2 54.7 113 Nb2O5 170.0 114 SiO2 52.2 115 Nb2O5 48.7 116 SiO2 68.0 117 Nb2O5 58.8 118 SiO2 85.6 119 Nb2O5 61.8 120 SiO2 99.7 121 Nb2O5 63.0 122 SiO2 100.1

TABLE 5 FIG. 9 Layer Arrangement Coating Thickness (μm): 7.046 Nb2O5 (μm): 2.615 SiO2 (μm): 4.431 Total Layers: 82 Layer Material Thickness (nm) 1 Nb2O5 108.5 2 SiO2 164.2 3 Nb2O5 125.4 4 SiO2 205.9 5 Nb2O5 42.2 6 SiO2 261.3 7 Nb2O5 135.7 8 SiO2 117.3 9 Nb2O5 39.7 10 SiO2 107.8 11 Nb2O5 46.8 12 SiO2 81.7 13 Nb2O5 25.5 14 SiO2 60.0 15 Nb2O5 46.8 16 SiO2 160.9 17 Nb2O5 51.1 18 SiO2 93.6 19 Nb2O5 64.3 20 SiO2 85.2 21 Nb2O5 41.9 22 SiO2 54.5 23 Nb2O5 36.4 24 SiO2 86.5 25 Nb2O5 57.7 26 SiO2 102.3 27 Nb2O5 63.0 28 SiO2 100.1 29 Nb2O5 51.7 30 SiO2 66.7 31 Nb2O5 31.8 32 SiO2 62.6 33 Nb2O5 53.6 34 SiO2 93.8 35 Nb2O5 62.5 36 SiO2 84.5 37 Nb2O5 56.8 38 SiO2 63.2 39 Nb2O5 43.0 40 SiO2 52.1 41 Nb2O5 48.9 42 SiO2 74.9 43 Nb2O5 60.5 44 SiO2 89.9 45 Nb2O5 60.5 46 SiO2 82.3 47 Nb2O5 40.6 48 SiO2 51.8 49 Nb2O5 42.9 50 SiO2 79.2 51 Nb2O5 60.5 52 SiO2 96.4 53 Nb2O5 61.8 54 SiO2 87.7 55 Nb2O5 52.3 56 SiO2 62.1 57 Nb2O5 42.5 58 SiO2 62.7 59 Nb2O5 51.0 60 SiO2 85.4 61 Nb2O5 54.9 62 SiO2 109.8 63 Nb2O5 41.9 64 SiO2 230.5 65 Nb2O5 170.1 66 SiO2 141.5 67 Nb2O5 43.0 68 SiO2 123.0 69 Nb2O5 35.5 70 SiO2 57.9 71 Nb2O5 145.9 72 SiO2 91.3 73 Nb2O5 43.8 74 SiO2 129.6 75 Nb2O5 40.3 76 SiO2 164.8 77 Nb2O5 117.9 78 SiO2 42.4 79 Nb2O5 31.9 80 SiO2 201.0 81 Nb2O5 183.8 82 SiO2 262.7

PARTS LIST

-   10. Laser attenuator -   12. Light source -   14. Half-wave plate -   16. Polarizing beamsplitter -   20. Light dump element -   30. Optical element -   46, 48, 50, 52, 54. Graph -   56. Curve -   58. Curve -   60. Graph -   70. Substrate -   80 a 1, 80 a 2 . . . 80 z 1, 80 z 2. Layer -   A. Attenuation curve for the average of S- and P-polarized light     component -   D, D1, D2. Difference curve -   DS, DP. Deviation curve -   E, K1, K2. Inset -   P. Attenuation curve for P-polarized light component -   S. Attenuation curve for S-polarized light component -   λ₁, λ₂. Wavelength -   θ₁, θ₂. Angle 

The invention claimed is:
 1. An optical element comprising: at least one substrate having at least one surface; and a plurality of layers formed on the at least one surface of the at least one substrate, the plurality of layers including alternating first and second layers, the first layers having a first refractive index, n_(L), and the second layers having a second refractive index, n_(H), greater than the first refractive index, wherein the plurality of layers exhibit a spectral characteristic, the spectral characteristic providing, for incident light at a predetermined wavelength and directed to the optical element within a range of incident angles bounded by a first incident angle θ₁ and a second incident angle θ₂, wherein the first and second incident angles θ₁ and θ₂ are between 0 and 80 degrees and wherein the difference between the first and second incident angles θ₁ and θ₂ is at least 1 degree, a monotonic relation of the polarization-averaged attenuation of the incident light energy given by: Aθ _(n)=−log₁₀((Tp _(n) +Ts _(n))/2) wherein, for any incident angle θ_(n) that lies within the range between and including angles θ₁ and θ₂, Aθ_(n) is the corresponding polarization-averaged attenuation in terms of optical density, Tp_(n) is the transmission, at angle θ_(n), of light energy of a first polarization axis, and Ts_(n) is the transmission, at angle θ_(n), of light energy of a second polarization axis that is orthogonal to the first polarization axis, and −0.1 OD≦Ap _(n) −As _(n)≦+0.1 OD; wherein OD is optical density, Ap_(n)=−log₁₀(Tp_(n)) is the attenuation, at angle θ_(n), to light energy of the first polarization axis, and As_(n)=−log₁₀(Ts_(n)) is the attenuation, at angle θ_(n), to light energy of the second polarization axis that is orthogonal to the first polarization axis, and wherein the polarization-averaged attenuation Aθ_(n) at angle θ₁ is less than or equal to an optical density value of 0.2 and the polarization-averaged attenuation Aθ_(n) at angle θ₂ exceeds an optical density value of
 2. 2. The optical element of claim 1 wherein the difference between the first and second incident angles θ₁ and θ₂ exceeds 2 degrees.
 3. The optical element of claim 1 wherein the polarization-averaged attenuation at angle θ₂ exceeds an optical density value of
 3. 4. The optical element of claim 1 wherein the polarization-averaged attenuation at angle θ₂ exceeds an optical density value of
 4. 5. The optical element of claim 1 wherein −0.02 OD≦Ap _(n) −As _(n)≦+0.02 OD.
 6. The optical element of claim 1 wherein −0.01 OD≦Ap _(n) −As _(n)≦+0.01 OD.
 7. The optical element of claim 1 wherein the plurality of layers includes one or more of: SiO₂, Ta₂O₅, Nb₂O₅, HfO₂, TiO₂, and Al₂O₅.
 8. An optical element comprising: at least one substrate having at least one surface; and a plurality of layers formed on the at least one surface of the at least one substrate, the plurality of layers including alternating first and second layers, the first layers having a first refractive index, n_(L), and the second layers having a second refractive index, n_(H), greater than the first refractive index, wherein the plurality of layers exhibit a spectral characteristic, the spectral characteristic providing, for incident light at a predetermined wavelength and directed toward the optical element within a range of incident angles bounded by a first incident angle θ₁ and a second incident angle θ₂, wherein the first and second incident angles θ₁ and θ₂ are between 0 and 80 degrees and wherein the difference between the first and second incident angles θ₁ and θ₂ is at least 1 degree, substantially linear polarization-averaged attenuation of the incident light energy given by: Aθ _(n)=−log₁₀((Tp _(n) +Ts _(n))/2) wherein, for any incident angle θ_(n) that lies within the range between and including angles θ₁ and θ₂, Aθ_(n) is the corresponding polarization-averaged attenuation in terms of optical density, Tp_(n) is the transmission, at angle θ_(n), of light energy of a first polarization axis, and Ts_(n) is the transmission, at angle θ_(n), of light energy of a second polarization axis that is orthogonal to the first polarization axis, and wherein the polarization-averaged attenuation Aθ_(n) at angle θ₁ is less than or equal to an optical density value of 0.2 and the polarization-averaged attenuation Aθ_(n) at angle θ₂ exceeds an optical density value of 4; wherein −0.1 OD≦Ap _(n) −As _(n)≦+0.1 OD; wherein OD is the optical density, Ap_(n)=−log₁₀(Tp_(n)) is attenuation, at angle θ_(n), to light energy of the first polarization axis, and As_(n)=−log₁₀(Ts_(n)) is attenuation, at angle θ_(n), to light energy of the second polarization axis. 